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- J. CHRIS EILBECK
- 2003

where i = √ −1, the index j ranges over the 1D lattice. The lattice may be infinite (j = 0,±1,±2, . . .) or finite (j = 1, 2, . . . , f). In the latter case one usually assumes periodic boundary conditions, Aj+f = Aj . The quantity Aj = Aj(t) is the complex mode amplitude of the oscillator at site j, and γ is a anharmonic parameter. The connection with the… (More)

- J C EILBECK
- 1999

The discovery of classical and quantum completely integrable systems led to an increase in interest in the theory of Abelian functions in theoretical physics and applied mathematics. This area was considered traditionally as a field of pure mathematics. This new trend makes it necessary to reconsider classical results in the area from the point of view of… (More)

J. C. Eilbeck,1 V. Z. Enolski,2 S. Matsutani,3 Y. Ônishi4 and E. Previato5 1Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS UK, 2Institute of Magnetism, Vernadski blvd. 36, Kiev-142, Ukraine, 38-21-1 Higashi-Linkan, Sagamihara, 228-0811, Japan, 4Faculty of Humanities and Social… (More)

- J. C. EILBECK
- 2008

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, with the specific example of the cyclic curve, y = x + λ4x + λ3x + λ2x + λ1x + λ0 discussed in detail. We define generalisations of the Weierstrass σ and ℘ functions, along with additional classes of Abelian functions. In addition, we present the associated partial… (More)

- J C Eilbeck, V Z Enol 'skii, V B Kuznetsov, A V Tsiganov
- 2008

We consider a hierarchy of the natural type Hamiltonian systems of n degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of 2×2 matrices for the whole hierarchy and construct the associated linear r-matrix algebra with the r-matrix dependent on the… (More)

Numerical predictions of a simple myelinated nerve fiber model are compared with theoretical results in the continuum and discrete limits, clarifying the nature of the conduction process on an isolated nerve axon. Since myelinated nerve fibers are often arranged in bundles, this model is used to study ephaptic (nonsynaptic) interactions between impulses on… (More)

- J. C. EILBECK
- 2006

We develop the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus three. The specific example of the “purely trigonal”curve y = x +λ3x 3 +λ2x 2 +λ1x+λ0 is discussed in detail, including a list of the associated partial differential equations satisfied by the ℘ functions, and the derivation of two addition formulae.

- A M Vallet, J A Coles, J C Eilbeck, A C Scott
- The Journal of physiology
- 1992

1. Voltage signals of about 1 mV evoked in photoreceptors of the drone honey bee by shallow modulation of a background illumination of an intensity useful for behaviour are thought to be amplified by voltage-dependent Na+ channels. To elucidate the roles of the various membrane conductances in this amplification we have studied the effects of the Na+… (More)

- J C Eilbeck
- 1994

We give an analytical description of the locus of the two-gap elliptic potentials associated with the corresponding flow of the Calogero– Moser system. We start with the description of Treibich–Verdier two– gap elliptic potentials. The explicit formulae for the covers, wave functions and Lamé polynomials are derived, together with a new Lax representation… (More)

- F M Russell, J C Eilbeck
- 2008

We report the ejection of atoms at a crystal surface caused by energetic breathers which have travelled more than 10 unit cells in atomic chain directions. The breathers were created by bombardment of a crystal face with heavy ions. This effect was observed at 300K in the layered crystal muscovite, which has linear chains of atoms for which the surrounding… (More)