3,531 research outputs found
Sandpile model on a quenched substrate generated by kinetic self-avoiding trails
Kinetic self-avoiding trails are introduced and used to generate a substrate
of randomly quenched flow vectors. Sandpile model is studied on such a
substrate with asymmetric toppling matrices where the precise balance between
the net outflow of grains from a toppling site and the total inflow of grains
to the same site when all its neighbors topple once is maintained at all sites.
Within numerical accuracy this model behaves in the same way as the
multiscaling BTW model.Comment: Four pages, five figure
Precise toppling balance, quenched disorder, and universality for sandpiles
A single sandpile model with quenched random toppling matrices captures the
crucial features of different models of self-organized criticality. With
symmetric matrices avalanche statistics falls in the multiscaling BTW
universality class. In the asymmetric case the simple scaling of the Manna
model is observed. The presence or absence of a precise toppling balance
between the amount of sand released by a toppling site and the total quantity
the same site receives when all its neighbors topple once determines the
appropriate universality class.Comment: 5 Revtex pages, 4 figure
Extended states in 1D lattices: application to quasiperiodic copper-mean chain
The question of the conditions under which 1D systems support extended
electronic eigenstates is addressed in a very general context. Using real space
renormalisation group arguments we discuss the precise criteria for determining
the entire spertrum of extended eigenstates and the corresponding
eigenfunctions in disordered as well as quasiperiodic systems. For purposes of
illustration we calculate a few selected eigenvalues and the corresponding
extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for
the infinite copper-mean chain, only a single energy has been numerically shown
to support an extended eigenstate [ You et al. (1991)] : we show analytically
that there is in fact an infinite number of extended eigenstates in this
lattice which form fragmented minibands.Comment: 10 pages + 2 figures available on request; LaTeX version 2.0
Sandpile model on an optimized scale-free network on Euclidean space
Deterministic sandpile models are studied on a cost optimized
Barab\'asi-Albert (BA) scale-free network whose nodes are the sites of a square
lattice. For the optimized BA network, the sandpile model has the same critical
behaviour as the BTW sandpile, whereas for the un-optimized BA network the
critical behaviour is mean-field like.Comment: Five pages, four figure
Energy dissipation in sheared wet granular assemblies
Energy dissipation in sheared dry and wet granulates is considered in the presence of an externally applied confining pressure. Discrete element simulations reveal that for sufficiently small confining pressures, the energy dissipation is dominated by the effects related to the presence of cohesive forces between the particles. The residual resistance against shear can be quantitatively explained by a combination of two effects arising in a wet granulate: (i) enhanced friction at particle contacts in the presence of attractive capillary forces and (ii) energy dissipation due to the rupture and reformation of liquid bridges. Coulomb friction at grain contacts gives rise to an energy dissipation which grows linearly with increasing confining pressure for both dry and wet granulates. Because of a lower Coulomb friction coefficient in the case of wet grains, as the confining pressure increases the energy dissipation for dry systems is faster than for wet ones
Connecting protein and mRNA burst distributions for stochastic models of gene expression
The intrinsic stochasticity of gene expression can lead to large variability
in protein levels for genetically identical cells. Such variability in protein
levels can arise from infrequent synthesis of mRNAs which in turn give rise to
bursts of protein expression. Protein expression occurring in bursts has indeed
been observed experimentally and recent studies have also found evidence for
transcriptional bursting, i.e. production of mRNAs in bursts. Given that there
are distinct experimental techniques for quantifying the noise at different
stages of gene expression, it is of interest to derive analytical results
connecting experimental observations at different levels. In this work, we
consider stochastic models of gene expression for which mRNA and protein
production occurs in independent bursts. For such models, we derive analytical
expressions connecting protein and mRNA burst distributions which show how the
functional form of the mRNA burst distribution can be inferred from the protein
burst distribution. Additionally, if gene expression is repressed such that
observed protein bursts arise only from single mRNAs, we show how observations
of protein burst distributions (repressed and unrepressed) can be used to
completely determine the mRNA burst distribution. Assuming independent
contributions from individual bursts, we derive analytical expressions
connecting means and variances for burst and steady-state protein
distributions. Finally, we validate our general analytical results by
considering a specific reaction scheme involving regulation of protein bursts
by small RNAs. For a range of parameters, we derive analytical expressions for
regulated protein distributions that are validated using stochastic
simulations. The analytical results obtained in this work can thus serve as
useful inputs for a broad range of studies focusing on stochasticity in gene
expression
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