Calculation of a characteristic fractal dimension in the one-dimensional random field ising model

By exploiting the connection with the problem of a repeller in a one dimensional map a new method is applied to calculate a fractal dimension characterising the local field. It is determined analytically in powers of the strength of the random field and also by an iteration procedure.     

One-dimensional random field Ising model and discrete stochastic mappings

Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.Contribution to the symposium Statistical Mechanics of Phase Transitions—Mathematical and Physical Aspects, Trebo, CSSR, September 1–6, 1986.     

Network description of the immune system: Dormant B cells stabilize cycles

The role of dormant B cells and cycles is analyzed in the context of a Lotka-Volterra network. It is shown that dormant B cells stabilize a cycle and that in this way both cooperate to preserve the internal image (memory) of an antigen. The network is embedded in a hierarchical scheme which allows adaptation, learning, and innovation by biased and random mutation.     

Solvability of a Commutative Algebra which Satisfies (x 2)2 = 0

We studied the solvability of the algebra which satisfies the polynomial identity (x ²)² = 0. We believe that, if A is a finite dimensional commutative algebra over a field F of characteristic not 2 which satisfies (x ²)² = 0 for all x ∈ A, then A is solvable. In this article we proved this when dim  _F A ≤ 7.     

Groups with bounded representation degree

Let Gbe a group and let K be a field of characteristic p> 0. If all irreducible representations of the group algebra K[G] have finite degree < n, then we show that G has a subgroup A with |G:A| bounded by a function of nand such that all the irreducible representations of K[A] have degree 1.     

Inductive current density perturbations to probe electron internal transport barriers in tokamaks

Improved electron energy confinement in tokamak plasmas, related to internal transport barriers, has been linked to nonmonotonic current density profiles. This is difficult to prove experimentally since usually the current profiles evolve continuously and current injection generally requires significant input power. New experiments are presented, in which the inductive current is used to generate positive and negative current density perturbations in the plasma center, with negligible input power. These results demonstrate unambiguously for the first time that the electron confinement can be modified significantly solely by perturbing the current density profile.     

Long-pulse improved central electron confinement in the TCV tokamak with electron cyclotron heating and current drive

Current profile tailoring by electron cyclotron heating (ECH) and current drive (ECCD) is used to improve central electron energy confinement in the TCV tokamak. Counter-ECCD on axis alone achieves this goal in a transient manner only. A stable scenario is obtained by a two-step sequence of off-axis ECH, which stabilizes magnetohydrodynamics modes, and on-axis counter-ECCD, which generates a flat or inverted current profile. This high-confinement regime, with central temperatures up to 9 keV (at a normalized beta(N) approximately 0.6), has been sustained for the entire duration of the heating pulse, or over 200 electron energy confinement times and 5 current redistribution times.     

Efficient exploration of reaction paths via a freezing string method

The ability to efficiently locate transition states is critically important to the widespread adoption of theoretical chemistry techniques for their ability to accurately predict kinetic constants. Existing surface walking techniques to locate such transition states typically require an extremely good initial guess that is often beyond human intuition to estimate. To alleviate this problem, automated techniques to locate transition state guesses have been created that take the known reactant and product endpoint structures as inputs. In this work, we present a simple method to build an approximate reaction path through a combination of interpolation and optimization. Starting from the known reactant and product structures, new nodes are interpolated inwards towards the transition state, partially optimized orthogonally to the reaction path, and then frozen before a new pair of nodes is added. The algorithm is stopped once the string ends connect. For the practical user, this method provides a quick and convenient way to generate transition state structure guesses. Tests on three reactions (cyclization of cis,cis-2,4-hexadiene, alanine dipeptide conformation transition, and ethylene dimerization in a Ni-exchanged zeolite) show that this "freezing string" method is an efficient way to identify complex transition states with significant cost savings over existing methods, particularly when high quality linear synchronous transit interpolation is employed.