1,679 research outputs found
Eulerian Walkers as a model of Self-Organised Criticality
We propose a new model of self-organized criticality. A particle is dropped
at random on a lattice and moves along directions specified by arrows at each
site. As it moves, it changes the direction of the arrows according to fixed
rules. On closed graphs these walks generate Euler circuits. On open graphs,
the particle eventually leaves the system, and a new particle is then added.
The operators corresponding to particle addition generate an abelian group,
same as the group for the Abelian Sandpile model on the graph. We determine the
critical steady state and some critical exponents exactly, using this
equivalence.Comment: 4 pages, RevTex, 4 figure
Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
We investigate the motion of a run-and-tumble particle (RTP) in one
dimension. We find the exact probability distribution of the particle with and
without diffusion on the infinite line, as well as in a finite interval. In the
infinite domain, this probability distribution approaches a Gaussian form in
the long-time limit, as in the case of a regular Brownian particle. At
intermediate times, this distribution exhibits unexpected multi-modal forms. In
a finite domain, the probability distribution reaches a steady state form with
peaks at the boundaries, in contrast to a Brownian particle. We also study the
relaxation to the steady state analytically. Finally we compute the survival
probability of the RTP in a semi-infinite domain. In the finite interval, we
compute the exit probability and the associated exit times. We provide
numerical verifications of our analytical results
Quenched Averages for self-avoiding walks and polygons on deterministic fractals
We study rooted self avoiding polygons and self avoiding walks on
deterministic fractal lattices of finite ramification index. Different sites on
such lattices are not equivalent, and the number of rooted open walks W_n(S),
and rooted self-avoiding polygons P_n(S) of n steps depend on the root S. We
use exact recursion equations on the fractal to determine the generating
functions for P_n(S), and W_n(S) for an arbitrary point S on the lattice. These
are used to compute the averages and over different positions of S. We find that the connectivity constant
, and the radius of gyration exponent are the same for the annealed
and quenched averages. However, , and , where the exponents
and take values different from the annealed case. These
are expressed as the Lyapunov exponents of random product of finite-dimensional
matrices. For the 3-simplex lattice, our numerical estimation gives ; and , to be
compared with the annealed values and .Comment: 17 pages, 10 figures, submitted to Journal of Statistical Physic
Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model
We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional
square lattice of lattice sizes up to L=4096. A detailed analysis of the
probability distribution of the size, area, duration and radius of the
avalanches will be given. To increase the accuracy of the determination of the
avalanche exponents we introduce a new method for analyzing the data which
reduces the finite-size effects of the measurements. The exponents of the
avalanche distributions differ slightly from previous measurements and
estimates obtained from a renormalization group approach.Comment: 6 pages, 6 figure
Observation of pseudogap in MgB2
Pseudogap phase in superconductors continues to be an outstanding puzzle that
differentiates unconventional superconductors from the conventional ones
(BCS-superconductors). Employing high resolution photoemission spectroscopy on
a highly dense conventional superconductor, MgB2, we discover an interesting
scenario. While the spectral evolution close to the Fermi energy is
commensurate to BCS descriptions as expected, the spectra in the wider energy
range reveal emergence of a pseudogap much above the superconducting transition
temperature indicating apparent departure from the BCS scenario. The energy
scale of the pseudogap is comparable to the energy of E2g phonon mode
responsible for superconductivity in MgB2 and the pseudogap can be attributed
to the effect of electron-phonon coupling on the electronic structure. These
results reveal a scenario of the emergence of the superconducting gap within an
electron-phonon coupling induced pseudogap.Comment: 4 figure
Inversion Symmetry and Critical Exponents of Dissipating Waves in the Sandpile Model
Statistics of waves of topplings in the Sandpile model is analysed both
analytically and numerically. It is shown that the probability distribution of
dissipating waves of topplings that touch the boundary of the system obeys
power-law with critical exponent 5/8. This exponent is not indeendent and is
related to the well-known exponent of the probability distribution of last
waves of topplings by exact inversion symmetry s -> 1/s.Comment: 5 REVTeX pages, 6 figure
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