The Institute of Mathematical Sciences
C. I. T. Campus, Taramani, Chennai 600 113
Programme
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Garani Ananthakrishna
Materials Research Centre and Centre for Condensed Matter Theory,
Indian Institute of Science, Bangalore - 560012
Martensitic transformations
often display features that are typical of a second order transformation
even though they are first order. For instance, the power law
statistics of acoustic emission signals and the precursor effect
seen much above the transition temperature are signatures of critical fluctuations.
On the other hand, experiments on acoustic emission (AE) show
that the transformation proceeds in a jerky manner which indicates
that it is a threshold transformation. Recently a two dimensional
model was introduced to explain the power law statistics of AE signals.
The essential ingredients of the model is that it includes threshold dynamics,
inertial effects, long range interactions between transformed regions and
dissipation arising from the rapid movements of the interfaces [1].
Another equally interesting
unexplained feature of athermal martensites is the repetitive bursts of
AE signals when the sample is cycled in a small temperature interval.
Concomitantly, the associated domains grow and shrink. The above model
is also found to explain these features, thus offering an insight into
the shape memory effect. We show that the model can explain
the precursor effect also.
References
1. R. Ahluwalia and G.Ananthakrishna, Phys. Rev. Lett 86, 4076
(2001).
2. S. Sreekala and G. Ananthakrishna, in print Phys. Rev. Lett (2003).
Department of Physics, Indian Institute of Technology - Madras, Chennai - 600036
To be announced
Mustansir Barma
Theoretical Physics Group, Tata Institute of Fundamental Research, Mumbai - 400005
Bikas K. Chakrabarti
Saha Institute of Nuclear Physics, Kolkata - 700064
We study the time evolution of the fraction of broken fibers in a loaded
Random Fiber Bundle Model having the strength of fibers distributed uniformly
or linearly within a finite interval, under the assumption of global load
sharing. Solution of the equation of motion near the fixed point, for loads
below the failure load, gives both static and dynamic critical behaviour
near the failure load. Universality of the critical behaviour is demonostrated.
It also gives precise expression for the amount of plastic deformation
upto the failure point.
Theoretical Physics Group, Tata Institute of Fundamental Research, Mumbai - 400005
To be announced
Alex Hansen
Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway
There is mounting evidence that brittle fracture surfaces are self affine
with roughness exponents that are universal. During mode one fracture
(cleavage), an in-plane roughness exponent may be observed in addition to
the out-of-plane roughness exponent. While the latter is close to 0.8
(with some exceptions), the former turns out to be close to 0.6. Since the
mid nineties, numerous numerical and theoretical studies of this problem
has been published. They have systematically found an in-plane roughness
exponent significantly lower than the observed value - typically close to
1/3.
I will in this talk present a numerical study of the in-plane roughness
exponent based on a Green function technique which differs from the one
used previously. With this technique, certain linearizations are avoided,
and we find a roughness exponent of 0.6 in accordance with the experimental
findings.
I will also present a theory based on a correlated percolation process
which predicts a roughness exponent of 0.61 for the in-plane roughness
exponent.
References
[1] A. Hansen and J. Schmittbuhl, Phys. Rev. Lett. 90, 045504 (2003).
[2] J. Schmittbuhl, A. Hansen and G. G. Batrouni, Phys. Rev. Lett. 90,
045505 (2003).
Jun-ichi Inoue
Complex Systems Engineering, Graduate School of Engineering, Hokkaido University, Sapporo, Japan
Problems of massive information processing including image restoration
or error-correcting codes are described by Markov random fields or Bayesian
belief networks which are sometimes refereed to as ``graphical models".
In these model systems, we should determine so-called hyper-parameters
which specify the posterior distribution in the context of the Bayesian
inference. In such cases, EM algorithm (Expectation Maximum algorithm)
is widely used as one of major tools to obtain maximum likelihood estimates
from incomplete data sets. The EM algorithm maximizes the likelihood function
indirectly by iterating the E and M steps until some appropriate convergence
conditions are satisfied. However, the EM algorithm has the problem that
the solution converges to a local optimal due to the dependence of the
initial state of parameters in the posterior distribution. In order to
avoid this difficulty,
Ueda and Nakano, Streit and Luginbuhl (1994) proposed DAEM algorithm
(Deterministic Annealing EM algorithm) independently. They replaced the
posterior distribution appearing in so-called Q-function with the probability
that maximizes the Boltzmann-Shannon entropy under some macroscopic constraints.
The probability they obtained contains a control parameter corresponding
to inverse-temperature in the statistical-mechanical context. In their
modified EM algorithm, the inverse-temperature $\beta$ is controlled as
$\beta \to 1$ to reduce the dependence of the initial condition.
Under the influence of their study, we modified the posterior
distribution by means of maximizing the non-extensive Tsallis entropy (Tabushi
and Inoue (2001)). In our posterior distribution, a parameter $q$, which
represents non-extensivity of the entropy, is controlled as $q \to 1$ to
reduce the strong dependence of the initial conditions. We carried out
computer simulations to check the usefulness of our algorithm and found
that our algorithm enable us to infer the hyper-parameters correctly for
the Gaussian mixture density estimation problem for which the EM or the
DAEM algorithm fails to estimate the true values. However, the results
depend on the data we used and we need much more ``tight" evaluation of
the performance. With this motivation in mind, we apply our algorithm to
Gaussian mixture estimation problems under some additive noises to investigate
the performance analytically. In the large data limit, we derive the averaged
update equations with respect to hyper-parameters, marginal likelihood,
etc. exactly. In addition to the estimation of the hyper-parameters, we
also evaluate the FT estimation (Finite Temperature estimation) andthe
MAP estimation (Maximum A Posteriori estimation) for estimation problems
of the original data generated by the Gaussian mixture itself.Our analysis
supports the result which was already obtained by us via computer simulations.
Kimmo Kaski
Laboratory of Computational Engineering, Helsinki University of Technology, Espoo, Finland
In 1952 one of the key scientists of the 20th century, Alan Turing, proposed a system of reaction-diffusion equations describing chemical reactions and diffusion to account for morphogenesis, i.e., the development of patterns, shapes and structures found in nature. These complex systems have been used in explaining, e.g., patterns on animal coatings and the segmentation in embryos. Here we will discuss our study of such pattern formations and their structures obtained through numerical simulation of the Turing mechanism in two and three dimensions. We have investigated the dependence of resulting structures on the system parameters, transitions between these structures, and percolation of chemicals in the system. In addition, we have studied the effect of random noise on developing these structures because noise plays a crucial role in the behaviour of various systems in nature. For example we have observed melting or stabilization of well order patterns due to noise. In summary Turing type - relatively simple - systems can result in complex morphological patterns remarkably similar to various patterns found in nature.
References
A.M. Turing, Phil. Trans R. Soc. Lond. B237, 37-72 (1952).
T. Leppänen, M. Karttunen, K. Kaski, R.A. Barrio, and L. Zhang,
Physica D.168-169, 35-44 (2002).
Janos Kertesz
Department of Theoretical Physics, Budapest University of Technology, Hungary
We discuss briefly the method of contact dynamics as an alternative
to more traditional approaches and show how spurious oscillations occur.
We investigate static packings of hard discs and spheres and analyse the
force network. We find that the force distribution is bimodal: Large forces
follow an exponential law while the distribution of forces weaker than
the average is history dependent. In the zero friction limit the packing
is isostatic. Switching on friction enhances the force fluctuations and
leads to hyperstatic packings, i.e. to ambiguity in the force network construction.
The dependence of the fluctuations on the friction is nontrivial where
size effects play an important role.
S. S. Manna
Satyendra Nath Bose National Centre for Basic Sciences (SNBNCBS), Kolkata - 700098
Sandpile models have been studied on random lattices where the
toppling matrices are random but can be either symmetric or asymmetric.
It is argued that a detailed balance between the number of sandgrains required
by a site to topple (input) and the number of grains that come out of the
site in a toppling (output) determines which universality class the model
belongs. In the symmetric case the balance is maintained where as in the
asymmetric case it is not and they behave as the BTW or the stochastic
sandpile models.
K. P. N. Murthy
Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102
Self Avoiding Walks (SAW) generated by nonreversing blind ants, constitute
an athermal ensemble of linear homopolymer configurations. Equilibrium
properties at any finite temperatures are calculated from this ensemble
by summing over the Boltzmann weights, leading to what is referred to as
Interacting Self Avoiding Walks (ISAW). There are however kinetic growth
models that generate nonequilibrium ensembles. The Kinetic Growth Walks
(KGW) for example generate polymers that have grown faster than they
could relax. Nevertheless the KGW belongs to the same universality class
as SAW. The Interacting Growth Walks (IGW) generalize the idea of KGW by
including a growth temperature which controls locally the growth process.
IGW belongs to the same universality class as ISAW. It predicts correctly
the phase transition from the extended phase at high temperature
to a collapsed phase at low temperature. At the transition point we have
the theta polymer phase. The correlation exponent, the entropic exponent
and the crossover exponent in the three phases are also predicted correctly
by the IGW ensemble. For a given growth parameter we calculate numerically
through Monte Carlo simulation, the typical bath temperature
to which the IGW ensemble corresponds to. Centering around the calculated
bath temperature we carry out multicanonical reweighting to extract
equilibrium properties. On the other hand if we interpret the spread in
the bath temperature distribution as arising due to energy disorder, we
can calculate the specific heat which shows a sharp peak at the collapse
transition and a broad hump representing perhaps the presence of dynamically
generated frozen disorder, like in glasses.
References
S. L. Narasimhan, P. S. R. Krishna, K. P. N. Murthy and M. Ramanadham,
Phys Rev E 65, 010801 (2002).
S. L. Narasimhan, V. Sridhar, P. S. R. Krishna and K. P. N. Murthy,
Physica A 320, 51 (2003).
S. L. Narasimhan, P. S. R. Krishna, A. K. Rajarajan and K. P.
N. Murthy, Phys Rev E 67, 011802 (2003)
Rahul Pandit
Department of Physics, Indian Institute of Science, Bangalore - 560012
We give an overview of our studies of spiral turbulence and spatiotemporal
chaos in two excitable media, namely, (a) the oxidation of CO on Pt(110)
and (b) models for ventricular fibrillation in mammalian hearts.
Department of Physics, North Eastern Hill University, Shillong
To be announced
Sudeshna Sinha
Institute of Mathematical Sciences, Chennai - 600113
We show how threshold activated coupling of chaotic elements yields
collective behaviour ranging from exact spatio-temporal cycles of all orders,
to scaling regimes (marked by 1/f spectra and power law distributions),
under varying theshold levels. We then go on to demonstrate how thresholding
can provide a powerful tool for spatiotemporal control of chaotic lattices.
Sorin Solomon
Racah Institute of Physics, Hebrew University of Jerusalem, Israel
The discrete microscopic structure of the macroscopic objects was postulated since the time of Democritus. The crucial relevance of this fact for their actual properties became evident in the modern times starting with the Dalton laws in chemistry and culminated in physics with the statistical atomic-molecular mechanics of Boltzmann and Maxwell.
It turns out that in systems with auto-catalytic interactions (proliferation,
contagion, information spread) as most biological and social systems are,
the discreteness of the
elementary components and interactions (e.g. giving birth to a new
individual, informing a neighbor of a new product, adoption of a new idea
by an individual, contracting a disease) is even more crucial.
Indeed, for many of such systems the continuum approximation (ignoring
microscopic discreteness) would predict an uniform, static (life-less,
trade-less, idea-less) asymptotic state. In reality such systems present
generically emergent spatio-temporal localized objects with unexpected
collective dynamical properties: adaptability, resilience and sustainability.
I will present the generic mechanism in terms of renormalization group,
some recent mathematical proofs based on branching random walks and
mainly applications to real phenomena.
References
N. M. Shnerb, P. Sarah, H. Lavee, and S. Solomon, Phys. Rev. Lett.
90, 038101 (2003)
Sorin Solomon and Moshe Levy, Quantitative Finance Vol 3 No 1, C12
S. Solomon and E. Shir, Europhysics News 34/2 (2003) in print.
O. Malcai, O. Biham, P. Richmond, and S. Solomon, Phys. Rev. E 66,
031102 (2002)
S. Solomon and P. Richmond, Eur. Phys. J. B 27, 257-261 (2002)
Yoram Louzoun, Sorin Solomon, Henri Atlan and Irun. R. Cohen, Physica
A , 297 (1-2) (2001) pp. 242-252
Nadav M. Shnerb, Yoram Louzoun, Eldad Bettelheim, and Sorin Solomon,
Proc. Natl. Acad. Sci. USA, Vol. 97, Issue 19, p 10322, (2000)
Ordinary miracles, New Scientist magazine, 06 May 2000.
http://shum.cc.huji.ac.il/~sorin/mir.htm
Dietrich Stauffer
Department of Theoretical Physics, University of Cologne, Cologne, Germany
We discuss the influence of information contagion on the dynamics of
choices
in social networks of heterogeneous buyers. Starting from an inhomogeneous
cellular automata model of buyers dynamics, we show that when agents try
to adjust their reservation price, the tatonement process does not converge
to equilibrium at some intermediate market share and that large amplitude
fluctuations are actually observed.
When the tatonnement dynamics is slow with respect to the contagion
dynamics, large periodic oscillations reminiscent of business cycles appear.