Stable manifolds and homoclinic points near resonances in the restricted three-body problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers $p$ and $q$, if its period around the heavier primary is approximately $2\pi p/q$, and by its approximate eccentricity $e$. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with $q/p$ equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any $\mu$ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for $\mu$ small enough in the unaveraged restricted three-body problem

Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings

The dynamical properties at T=0 of the one-dimensional (1D) s=1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling are investigated by means of the recursion method in combination with techniques of continued-fraction analysis. The focus is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega), which describe (for q=\pi) the fluctuations of the N\'eel and dimer order parameters, respectively. We calculate (via weak-coupling continued-fraction analysis) the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the spin-fluid phase, which is realized for planar $nn$ anisotropy and sufficiently weak nnn coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but not to S_{DD}(q,\omega).Comment: RevTex file (7 pages), 8 figures (uuencoded ps file) available from author

Systematic Mapping of the Hubbard Model to the Generalized t-J Model

The generalized t-J model conserving the number of double occupancies is constructed from the Hubbard model at and in the vicinity of half-filling at strong coupling. The construction is realized by a self-similar continuous unitary transformation. The flow equation is closed by a truncation scheme based on the spatial range of processes. We analyze the conditions under which the t-J model can be set up and we find that it can only be defined for sufficiently large interaction. There, the parameters of the effective model are determined.Comment: 16 pages, 13 figures included. v2: Order of sections changed. Calculation and discussion of apparent gap in Section IV.A correcte

The resistance of randomly grown trees

Copyright @ 2011 IOP Publishing Ltd. This is a preprint version of the published article which can be accessed from the link below.An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability p or two edges with probability 1 − p. With each edge having a resistance equal to 1 omega, the total resistance Rn between the root vertex and a busbar connecting all the vertices at the nth level is considered. A dynamical system is presented which approximates Rn, it is shown that the mean value (Rn) for this system approaches (1 + p)/(1 − p) as n → ∞, the distribution of Rn at large n is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate Rn; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with |(Rn) − (1 + p)/(1 − p)| ∼ n−1/2.Engineering and Physical Sciences Research Council (EPSRC

COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.

The finite size effects of the dynamical structure factors in the XXZ-model are studied in the euclidean time $(\tau)$-representation. Away from the critical momentum $p=\pi$ finite size effects turn out to be small except for the large $\tau$ limit. The large finite size effects at the critical momentum $p=\pi$ signal the emergence of infrared singularities in the spectral $(\omega)$-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse

Canonical, squeezed and fermionic coherent states in a right quaternionic Hilbert space with a left multiplication on it

Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that various classes of coherent states such as the canonical coherent states, pure squeezed states, fermionic coherent states can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstrate squeezed states can be defined on the same Hilbert space, but the noncommutativity of quaternions prevents us in getting the desired results.Comment: Conference paper. arXiv admin note: text overlap with arXiv:1704.02946; substantial text overlap with arXiv:1706.0068

Feasibility of Using a Web-Based Nutrition Intervention Among Residents of Multiethnic Working-Class Neighborhoods

Introduction: Using the Internet to promote behavior change is becoming more desirable as Internet use continues to increase among diverse audiences. Yet we know very little about whether this medium is useful or about different strategies to encourage Internet use by various populations. This pilot study tested the usefulness of a Web-based intervention designed to deliver nutrition-related information to and increase fruit and vegetable consumption among adults from working-class neighborhoods. Methods: Participants (N = 52) had access to the Web site for 6 weeks and received three e-mail reminders encouraging them to eat fruits and vegetables. The Web site provided information about overcoming barriers to healthy eating, accessing social support for healthy eating, setting goals for healthy eating, and maintaining a healthy diet, including recipes. We collected data on participants' use of the Web site, their Internet access and use, and their fruit and vegetable consumption. Results: The mean age of the participants was 46 years, 73% were white, 46% did not have a college degree, and 12% had household incomes at or below 185% of the federal poverty index. They reported consuming an average of 3.4 servings of fruits and vegetables per day. More than half of the participants owned a computer, 75% logged onto the Web site at least once, and those who visited the site averaged 3.8 visits and viewed an average of 24.5 pages. The number of log-ons per day declined over the study period; however, reminder e-mails appeared to motivate participants to return to the Web site. Roughly 74% of participants viewed information on goal setting, 72% viewed information on dietary tracking, and 56% searched for main course recipes. Conclusion: The results of this pilot study suggest that Internet-based health messages have the potential to reach a large percentage of adults from working-class neighborhoods who have access to the Internet

Combined BRAFV600E- and SRC-inhibition induces apoptosis, evokes an immune response and reduces tumor growth in an immunocompetent orthotopic mouse model of anaplastic thyroid cancer

Anaplastic (ATC) and refractory papillary thyroid cancer (PTC) lack effective treatments. Inhibition of either oncogenic BRAF or SRC has marked anti-tumor effects in mouse models of thyroid cancer, however, neither drug induces notable apoptosis. Here we report that the SRC-inhibitor dasatinib further sensitizes BRAFV600E-positive thyroid cancer cells to the BRAFV600E-inhibitor PLX4720. Combined treatment with PLX4720 and dasatinib synergistically inhibited proliferation and reduced migration in PTC and ATC cells. Whereas PLX4720 did not induce robust apoptosis in thyroid cancer cells, combined treatment with dasatinib induced apoptosis in 4 of 6 lines. In an immunocompetent orthotopic mouse model of ATC, combined PLX4720 and dasatinib treatment significantly reduced tumor volume relative to PLX4720 treatment alone. Immune cell infiltration was increased by PLX4720 treatment and this effect was maintained in mice treated with both PLX4720 and dasatinib. Further, combined treatment significantly increased caspase 3 cleavage in vivo relative to control or either treatment alone. In conclusion, combined PLX4720 and dasatinib treatment induces apoptosis, increases immune cell infiltration and reduces tumor volume in a preclinical model of ATC, suggesting that the combination of these FDA-approved drugs may have potential for the treatment of patients with ATC or refractory PTC

Continuous slice functional calculus in quaternionic Hilbert spaces

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic $C^*$--algebras and to define, on each of these $C^*$--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic

Charge and spin dynamics in the one-dimensional t−Jzt-J_z and t−Jt-J models

The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttinger-liquid ground state of the 1D $t-J$ model is assessed by comparison with the same quantities in the 1D $t-J_z$ model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At $J_z/t=0^+$ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. The $t-J_z$ charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the $t-J$ model. In the $t-J_z$ model, phase separation is accompanied by N\'eel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the $t-J$ model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by 2-spinon excitations) in the phase-separated state.Comment: 11 pages (RevTex). 14 Figures available from author