3,956 research outputs found
Integrability of Dirac reduced bi-Hamiltonian equations
First, we give a brief review of the theory of the Lenard-Magri scheme for a
non-local bi-Poisson structure and of the theory of Dirac reduction. These
theories are used in the remainder of the paper to prove integrability of three
hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some
generalized Drinfeld-Sokolov hierarchies.Comment: 15 pages. Corrected some typos and added missing equations in Section
5 for g=sl_n, n>
Adaptive walks in a gene network model of morphogenesis: insights into the Cambrian explosion
The emergence of complex patterns of organization close to the Cambrian
boundary is known to have happened over a (geologically) short period of time.
It involved the rapid diversification of body plans and stands as one of the
major transitions in evolution. How it took place is a controversial issue.
Here we explore this problem by considering a simple model of pattern formation
in multicellular organisms. By modeling gene network-based morphogenesis and
its evolution through adaptive walks, we explore the question of how
combinatorial explosions might have been actually involved in the Cambrian
event. Here we show that a small amount of genetic complexity including both
gene regulation and cell-cell signaling allows one to generate an extraordinary
repertoire of stable spatial patterns of gene expression compatible with
observed anteroposterior patterns in early development of metazoans. The
consequences for the understanding of the tempo and mode of the Cambrian event
are outlined.Comment: to appear in International Journal of Developmental Biology, special
issue on Evo-Devo (2003
On classification of Poisson vertex algebras
We describe a conjectural classification of Poisson vertex algebras of CFT
type and of Poisson vertex algebras in one differential variable (= scalar
Hamiltonian operators)
Testing hypotheses of the cause of peripheral thinning of the Greenland Ice Sheet: is land-terminating ice thinning at anomalously high rates?
Recent observations have shown that the periphery of the Greenland ice sheet (GrIS) is thinning rapidly and that this thinning is greatest around marine-terminating outlet glaciers. Several theories have been proposed which provide a link between climate and ice thinning. We present surface elevation change (<i>dh/dt</i>) data from NASA's Program for Arctic Regional Climate Assessment (PARCA) laser altimetry surveys for fourteen and eleven of the largest outlet glaciers in Southern Greenland from 1993 to 1998 and 1998 to 2006 respectively to test the applicability of these theories to the GrIS. <br><br> Initially, outlet glacier <i>dh/dt</i> data are compared with data from concurrent surveys over inland ice (slow flowing ice that is not obviously draining into an outlet glacier) to confirm the effect of ice flow on surface thinning rates. Land-terminating and marine-terminating outlet glacier <i>dh/dt</i> data are then compared from 1993 to 1998 and from 1998 to 2006. Finally, ablation anomalies (the difference between the "normal" ablation rate from 1970 to 2000 and the ablation rate in the time period of interest) calculated with a positive degree day model are compared to both marine-terminating and land-terminating outlet glacier <i>dh/dt</i> data. <br><br> Our results support earlier conclusions that certain marine-terminating outlet glaciers have thinned much more than land-terminating outlet glaciers during both time periods. Furthermore we show that these differences are not limited to the largest, fastest-flowing outlet glaciers – almost all marine-terminating outlet glaciers are thinning more than land-terminating outlet glaciers. There was a four fold increase in mean marine-terminating outlet glacier thinning rates below 1000 m elevation between the periods 1993 to 1998 and 1998 to 2006, while thinning rates of land-terminating outlet glaciers remained statistically unchanged. This suggests that a change in a controlling mechanism specific to the thinning rates of marine-terminating outlet glaciers occurred in the late 1990s and that this change did not affect thinning rates of land-terminating outlet glaciers. <br><br> Thinning rates of land-terminating outlet glaciers are statistically the same as ablation anomalies, while thinning rates of marine-terminating outlet glaciers are not. Thinning of land-terminating outlet glaciers therefore seems to be a response to changes in local mass balance (principally increases in air temperature) while thinning of marine-terminating outlet glaciers is principally controlled by ice dynamics. The mechanism by which this dynamic thinning occurs is still not clear although its association with marine-terminating outlet glaciers suggests perturbations at marine termini (calving) as the likely cause
Quantitative analysis of Clausius inequality
In the context of driven diffusive systems, for thermodynamic transformations
over a large but finite time window, we derive an expansion of the energy
balance. In particular, we characterize the transformations which minimize the
energy dissipation and describe the optimal correction to the quasi-static
limit. Surprisingly, in the case of transformations between homogeneous
equilibrium states of an ideal gas, the optimal transformation is a sequence of
inhomogeneous equilibrium states.Comment: arXiv admin note: text overlap with arXiv:1404.646
Minimum dissipation principle in stationary non equilibrium states
We generalize to non equilibrium states Onsager's minimum dissipation
principle. We also interpret this principle and some previous results in terms
of optimal control theory. Entropy production plays the role of the cost
necessary to drive the system to a prescribed macroscopic configuration
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