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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear stability analysis of inviscid flows in three dimensions: Incompressible fluids and barotropic fluids (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 3369-3382 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Using the energy-conserved quantity method developed by Arnol'd [Dokl. Mat. Nauk 162, 773 (1965); Am. Math. Soc. Trans. 19, 267 (1969)] a study was made of the nonlinear stability of two inviscid fluid flows in three dimensions: (1) flow of a homogeneous fluid and (2) flow of a fluid whose energy density depends on the mass density alone (a so-called barotropic fluid). In order to implement the Arnol'd technique one must identify the quantities conserved by the flow in addition to the total energy. In the case of the two flows considered, the conserved quantities cannot be expressed in terms of the usual Eulerian variables—fluid velocity and mass density—alone. Instead the introduction of the Lagrangian labels of the fluid elements is required. A complete description of these conserved quantities, in both Eulerian and Lagrangian specifications of the fluid, is provided. The phase space of the flow is the entire Hamiltonian phase space expressed in either canonical or noncanonical variables. The nature of the flows to which the Arnol'd method is applicable is discussed in some depth. It was discovered that only time independent Eulerian flows can be discussed by the method; this result is given a general Hamiltonian context. The allowed Eulerian equilibria are displayed in detail. Finally, having the formal structure of these flows well in hand, it is shown that they are not, in three dimensions, formally stable. This results from a particle vortex stretching mechanism which is identified. The nature of the indicated instability is not revealed by this work, but may well be a slowly evolving Arnol'd diffusion kind of breakdown of the equilibrium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866469
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  • 2
    Electronic Resource
    Electronic Resource
    Hamiltonian formulation of inviscid flows with free boundaries (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 2802-2809 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The formulation of the Hamiltonian structures for inviscid fluid flows with material free surfaces is presented in both the Lagrangian specification, where the fundamental Poisson brackets are canonical, and in the Eulerian specification, where the dynamics is given in noncanonical form. The noncanonical Eulerian brackets are derived explicitly from the canonical Lagrangian brackets. The Eulerian brackets are, with the exception of a single term at each material free surface separating flows in different phases, identical to those for isentropic flow of a compressible, inviscid fluid. The dynamics of the free surface is located in the Hamiltonian and in the definition of the Eulerian variables of mass density, ρ(x, t), momentum density, M(x,t) [which is ρ times the fluid velocity v(x,t)], and the specific entropy, σ(x,t). The boundary conditions for the Eulerian variables and the evolution equations for the free surfaces come from the Euler equations of the flow. This construction provides a unified treatment of inviscid flows with any number of free surfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866987
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  • 3
    Electronic Resource
    Electronic Resource
    Phase space density representation of inviscid fluid dynamics (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2952-2964 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A formulation of inviscid fluid dynamics based on the density F(x,v,t) in a single-particle phase space [x=(x1,x2,x3), v=(v1,v2,v3)] is presented. This density evolves in time according to a Poisson bracket of F with H(x,v,t)—a Hamiltonian in the same single-particle phase space. Compressible flows of barotropic fluid and homogeneous, incompressible flows are disscussed. The main advantage of the phase space density formulation over either Euler or Lagrange formulations is the algebraic and conceptual ease in making fully Hamiltonian approximations to the flow by altering H(x,v,t) and the Poisson brackets appropriately. The example of a shallow layer of rapidly rotating fluid where a Rossby number expansion is desired will be discussed in some detail. Changes of phase space coordinates that give an approximate H (expanded in Rossby number) and exact Poisson brackets will be exhibited. The resulting quasigeostrophic equations for F are two-dimensional partial differential equations to every order in Rossby number. The extension to multiple layers will be presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866073
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  • 4
    Electronic Resource
    Electronic Resource
    Dopamine modulation of spike dynamics in bursting neurons (2005)
    Oxford, UK : Blackwell Science Ltd
    European journal of neuroscience 21 (2005), S. 0 
    Details
    ISSN: 1460-9568
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Medicine
    Notes: The pyloric network of the lobster stomatogastric ganglion is a prime example of an oscillatory neural circuit. In our previous study on the firing patterns of pyloric neurons we observed characteristic temporal structures termed ‘interspike interval (ISI) signatures’ which were found to depend on the synaptic connectivity of the network. Dopamine, a well-known modulator of the pyloric network, is known to affect inhibitory synapses so it might also tune the fine temporal structure of intraburst spikes, a phenomenon not previously investigated. In the recent work we study the DA modulation of ISI patterns of two identified pyloric neurons in normal conditions and after blocking their glutamatergic synaptic connections. Dopamine (10–50 µm) strongly regularizes the firing of the lateral pyloric (LP) and pyloric dilator (PD) neurons by increasing the reliability of recurrent spike patterns. The most dramatic effect is observed in the LP, where precisely replicated spike multiplets appear in a normally ‘noisy’ neuron. The DA-induced regularization of intraburst spike patterns requires functional glutamatergic inputs to the LP neuron and this effect cannot be mimicked by simple intracellular depolarization. Inhibitory synaptic inputs arriving before the bursts are important factors in shaping the intraburst spike dynamics of both the PD and the LP neurons. Our data reveal a novel aspect of chemical neuromodulation in oscillatory neural networks. This effect sets in at concentrations lower than those affecting the overall burst pattern of the network. The sensitivity of intraburst spike dynamics to preceding synaptic inputs also suggests a novel method of temporal coding in neural bursters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1460-9568.2005.03894.x
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  • 5
    Electronic Resource
    Electronic Resource
    DYNAMICAL ISSUES IN HADRON PHYSICS (1974)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 229 (1974), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1974.tb20536.x
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  • 6
    Electronic Resource
    Electronic Resource
    Book reviews (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 787-807 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458430
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  • 7
    Electronic Resource
    Electronic Resource
    Nonlinearity and chaos at work (1993)
    [s.l.] : Nature Publishing Group
    Nature 364 (1993), S. 672-673 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] CHAOS is moving out of the mathematics department and into engineering design. That was the take-home message to emerge from a symposium Nonlinearity and Chaos in Engineering Dynamics, IUTAM Symposium, University College London, UK. 19-23 July 1993. held last month. The possibilities offered by the ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/364672a0
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  • 8
    Electronic Resource
    Electronic Resource
    Nonlinear dynamics of the Great Salt Lake: system identification and prediction (1996)
    Springer
    Climate dynamics 12 (1996), S. 287-297 
    Details
    ISSN: 1432-0894
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A case study of the application of recent methods of nonlinear time series analysis is presented. The 1848–1992 biweekly time series of the Great Salt Lake (GSL) volume is analyzed for evidence of low dimensional dynamics and predictability. The spectrum of Lyapunov exponents indicates that the average predictability of the GSL is a few hundred days. Use of the false nearest neighbor statistic shows that the dynamics of the GSL can be described in time delay coordinates by four dimensional vectors with components lagged by about half a year. Local linear maps are used in this embedding of the data and their skill in forecasting is tested in split sample mode for a variety of GSL conditions: lake average volume, near the beginning of a drought, near the end of a drought, prior to a period of rapid lake rise. Implications for modeling low frequency components of the hydro-climate system are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00219502
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  • 9
    Electronic Resource
    Electronic Resource
    Nonlinear dynamics of the Great Salt Lake: system identification and prediction (1996)
    Springer
    Climate dynamics 12 (1996), S. 287-297 
    Details
    ISSN: 1432-0894
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract. A case study of the application of recent methods of nonlinear time series analysis is presented. The 1848–1992 biweekly time series of the Great Salt Lake (GSL) volume is analyzed for evidence of low dimensional dynamics and predictability. The spectrum of Lyapunov exponents indicates that the average predictability of the GSL is a few hundred days. Use of the false nearest neighbor statistic shows that the dynamics of the GSL can be described in time delay coordinates by four dimensional vectors with components lagged by about half a year. Local linear maps are used in this embedding of the data and their skill in forecasting is tested in split sample mode for a variety of GSL conditions: lake average volume, near the beginning of a drought, near the end of a drought, prior to a period of rapid lake rise. Implications for modeling low frequency components of the hydro-climate system are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003820050109
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  • 10
    Electronic Resource
    Electronic Resource
    Modeling observed chaotic oscillations in bursting neurons: the role of calcium dynamics and IP3 (2000)
    Springer
    Biological cybernetics 82 (2000), S. 517-527 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. Chaotic bursting has been recorded in synaptically isolated neurons of the pyloric central pattern generating (CPG) circuit in the lobster stomatogastric ganglion. Conductance-based models of pyloric neurons typically fail to reproduce the observed irregular behavior in either voltage time series or state-space trajectories. Recent suggestions of Chay [Biol Cybern 75: 419–431] indicate that chaotic bursting patterns can be generated by model neurons that couple membrane currents to the nonlinear dynamics of intracellular calcium storage and release. Accordingly, we have built a two-compartment model of a pyloric CPG neuron incorporating previously described membrane conductances together with intracellular Ca2+ dynamics involving the endoplasmic reticulum and the inositol 1,4,5-trisphosphate receptor IP3R. As judged by qualitative inspection and quantitative, nonlinear analysis, the irregular voltage oscillations of the model neuron resemble those seen in the biological neurons. Chaotic bursting arises from the interaction of fast membrane voltage dynamics with slower intracellular Ca2+ dynamics and, hence, depends on the concentration of IP3. Despite the presence of 12 independent dynamical variables, the model neuron bursts chaotically in a subspace characterized by 3–4 active degrees of freedom. The critical aspect of this model is that chaotic oscillations arise when membrane voltage processes are coupled to another slow dynamic. Here we suggest this slow dynamic to be intracellular Ca2+ handling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050604
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