6,677 research outputs found
Homoclinic bifurcations in low-Prandtl-number Rayleigh-B\'{e}nard convection with uniform rotation
We present results of direct numerical simulations on homoclinic gluing and
ungluing bifurcations in low-Prandtl-number ()
Rayleigh-B\'{e}nard system rotating slowly and uniformly about a vertical axis.
We have performed simulations with \textit{stress-free} top and bottom
boundaries for several values of Taylor number () near the
instability onset. We observe a single homoclinic ungluing bifurcation, marked
by the spontaneous breaking of a larger limit cycle into two limit cycles with
the variation of the reduced Rayleigh number for smaller values of . A pair of homoclinic bifurcations, instead of one bifurcation, is
observed with variation of for slightly higher values of () in the same fluid dynamical system. The variation of the bifurcation
threshold with is also investigated. We have also constructed a
low-dimensional model which qualitatively captures the dynamics of the system
near the homoclinic bifurcations for low rotation rates. The model is used to
study the unfolding of bifurcations and the variation of the homoclinic
bifurcation threshold with .Comment: 6 pages, 7 figures, 1 tabl
Information theoretical study of cross-talk mediated signal transduction in MAPK pathways
Biochemical networks related to similar functional pathways are often
correlated due to cross-talk among the homologous proteins in the different
networks. Using a stochastic framework, we address the functional significance
of the cross-talk between two pathways. Our theoretical analysis on generic
MAPK pathways reveals cross-talk is responsible for developing coordinated
fluctuations between the pathways. The extent of correlation evaluated in terms
of the information theoretic measure provides directionality to net information
propagation. Stochastic time series and scattered plot suggest that the
cross-talk generates synchronization within a cell as well as in a cellular
population. Depending on the number of input and output, we identify signal
integration and signal bifurcation motif that arise due to inter-pathway
connectivity in the composite network. Analysis using partial information
decomposition quantifies the net synergy in the information propagation through
these branched pathways.Comment: Revised version, 17 pages, 5 figure
Role of relaxation time scale in noisy signal transduction
Intracellular fluctuations, mainly triggered by gene expression, are an
inevitable phenomenon observed in living cells. It influences generation of
phenotypic diversity in genetically identical cells. Such variation of cellular
components is beneficial in some contexts but detrimental in others. To
quantify the fluctuations in a gene product, we undertake an analytical scheme
for studying few naturally abundant linear as well as branched chain network
motifs. We solve the Langevin equations associated with each motif under the
purview of linear noise approximation and quantify Fano factor and mutual
information. Both quantifiable expressions exclusively depend on the relaxation
time (decay rate constant) and steady state population of the network
components. We investigate the effect of relaxation time constraints on Fano
factor and mutual information to indentify a time scale domain where a network
can recognize the fluctuations associated with the input signal more reliably.
We also show how input population affects both quantities. We extend our
calculation to long chain linear motif and show that with increasing chain
length, the Fano factor value increases but the mutual information processing
capability decreases. In this type of motif, the intermediate components are
shown to act as a noise filter that tune up input fluctuations and maintain
optimum fluctuations in the output. For branched chain motifs, both quantities
vary within a large scale due to their network architecture and facilitate
survival of living system in diverse environmental conditions.Comment: 14 pages, 6 figure
Dependence of acoustic surface gravity on disc thickness for accreting astrophysical black holes
For axially symmetric accretion maintained in hydrostatic equilibrium along
the vertical direction, we investigate how the characteristic features of the
embedded acoustic geometry depends on the background Kerr metric, and how such
dependence is governed by three different expressions of the thickness of the
matter flow. We first obtain the location of the sonic points and stationary
shock between the sonic points. We then linearly perturb the flow to obtain the
corresponding metric elements of the acoustic space-time. We thus construct the
causal structure to establish that the sonic points and the shocks are actually
the analogue black hole type and white hole type horizons, respectively. We
finally compute the value of the acoustic surface gravity as a function of the
spin angular momentum of the rotating black hole for three different flow
thicknesses considered in the present work. We find that for some flow models,
the intrinsic acoustic geometry, although in principle may be extended up to
the outer gravitational horizon of the astrophysical black hole, cannot be
constructed beyond a certain truncation radius as imposed by the expressions of
the thickness function of the corresponding flow.Comment: 22 pages, 9 figure
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