Dynamics of a single ion in a perturbed Penning trap: octupolar perturbation

Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincaré surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior.     

Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus

Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus. These include the correlation-length ratio x =lim _L (L)/L and the first four magnetization moment ratios V _2n = ²ⁿ / ^{2 n} . As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G*_2n . We confirm these predictions by a high-precision Monte Carlo simulation.     

Number of singularities of a foliation on

Let be a one dimensional foliation on a projective space, that is, an invertible subsheaf of the sheaf of sections of the tangent bundle. If the singularities of are isolated, Baum-Bott formula states how many singularities, counted with multiplicity, appear. The isolated condition is removed here. Let be the dimension of the singular locus of . We give an upper bound of the number of singularities of dimension , counted with multiplicity and degree, that may have, in terms of the degree of the foliation. We give some examples where this bound is reached. We then generalize this result for a higher dimensional foliation on an arbitrary smooth and projective variety.

     

Two‐step synthesis of new 1,2,4,5‐tetrahydrospiro‐[3H‐2‐benzazepine‐3,4′‐piperidines] from 4‐iminopiperidines

New spiro[3H‐2‐benzazepine‐3,4′‐piperidines] and their precursors, N‐substituted 4‐allyl‐4‐N‐benzyl‐aminopiperidines, have been prepared as potential psychotic agents from readily available 4‐iminopiperidines, by a sequence of reactions that included nucleophilic addition of Grignard reagents and Bronsted acid‐mediated intramolecular cyclisation. Some of the compounds prepared have been tested in albine mice for spontaneous motor activity. All compounds prepared were characterized by ir and ¹H nmr spectroscopies and cg‐ms spectrometry.     

Correlating backbone‐to‐backbone distance to ionic conductivity in amorphous polymerized ionic liquids

The morphology and ionic conductivity of poly(1‐n‐alkyl‐3‐vinylimidazolium)‐based homopolymers polymerized from ionic liquids were investigated as a function of the alkyl chain length and counterion type. In general, X‐ray scattering showed three features: (i) backbone‐to‐backbone, (ii) anion‐to‐anion, and (iii) pendant‐to‐pendant characteristic distances. As the alkyl chain length increases, the backbone‐to‐backbone separation increases. As the size of counterion increases, the anion‐to‐anion scattering peak becomes apparent and its correlation length increases. The X‐ray scattering features shift to lower angles as the temperature increases due to thermal expansion. The ionic conductivity results show that the glass transition temperature (T_g) is a dominant, but not exclusive, parameter in determining ion transport. The T_g‐independent ionic conductivity decreases as the backbone‐to‐backbone spacing increases. Further interpretation of the ionic conductivity using the Vogel–Fulcher–Tammann equation enabled the correlation between polymer morphology and ionic conductivity, which highlights the importance of anion hoping between adjacent polymer backbones. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Solutions to a gradient-dependent integro-differential parabolic problem arising in the pricing of financial options in a Lévy market

We study an integro-differential parabolic problem modeling a process with jumps arising in financial mathematics. Under suitable conditions, we prove the existence of solutions in a general domain by proving a uniform bound on an iterative sequence of solutions and then applying the Arzelà–Ascoli theorem.     

Synthesis of 2‐Spironaphtho[2,3‐b]pyranoquinones

A convenient procedure for the synthesis of 2‐spirobenzopyranoquinone 5 and its application to the preparation of spironaphtho[2,3‐b]pyranoquinones 6 and 7 is described.     

Engineering the Biosynthesis of the Polyketide-Nonribosomal Peptide Collismycin A for Generation of Analogs with Neuroprotective Activity

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Computing solutions to a forced KdV equation

In this paper a special forced Korteweg–de Vries (KdV) equation is considered. This equation is established by recent studies as a simple mathematical model of describing the physics of a shallow layer of fluid subject to external forcing. It serves as an analytical model of tsunami generation by submarine landslides. The bilinear form for this equation is obtained with the aid of Hirota’s method. Some of its one-, two- and three-soliton as well as breather-type soliton solutions and other interesting solutions are derived.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models VI. Square Lattice with Extra-Vertex Boundary Conditions

We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the boundary conditions that are obtained from an m×n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column. We provide numerical evidence that the partition-function zeros are becoming dense everywhere in the complex q-plane outside the limiting curve B_￥(sq)\mathcal{B}_{\infty}(\mathrm{sq}) for this model with ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the infinite-volume free energy is perfectly analytic in this region.