Periodic-Orbit Bifurcations and Superdeformed Shell Structure

We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in good agreement with quantum-mechanical results. We find that the bifurcations of some dominant short periodic orbits lead to an enhancement of the shell structure for "superdeformed" shapes related to those known from atomic nuclei.Comment: 4 pages including 3 figure

Nuclear fission: The "onset of dissipation" from a microscopic point of view

Semi-analytical expressions are suggested for the temperature dependence of those combinations of transport coefficients which govern the fission process. This is based on experience with numerical calculations within the linear response approach and the locally harmonic approximation. A reduced version of the latter is seen to comply with Kramers' simplified picture of fission. It is argued that for variable inertia his formula has to be generalized, as already required by the need that for overdamped motion the inertia must not appear at all. This situation may already occur above T=2 MeV, where the rate is determined by the Smoluchowski equation. Consequently, comparison with experimental results do not give information on the effective damping rate, as often claimed, but on a special combination of local stiffnesses and the friction coefficient calculated at the barrier.Comment: 31 pages, LaTex, 9 postscript figures; final, more concise version, accepted for publication in PRC, with new arguments about the T-dependence of the inertia; e-mail: [email protected]

Low density instability in a nuclear Fermi liquid drop

The instability of a Fermi-liquid drop with respect to bulk density distortions is considered. It is shown that the presence of the surface strongly reduces the growth rate of the bulk instability of the finite Fermi-liquid drop because of the anomalous dispersion term in the dispersion relation. The instability growth rate is reduced due to the Fermi surface distortions and the relaxation processes. The dependence of the bulk instability on the multipolarity of the particle density fluctuations is demonstrated for two nuclei $^{40}Ca$ and $^{208}Pb$.Comment: 12 pages, latex, 3 ps-figures, submitted to Phys. Rev.

Hormonal Signal Amplification Mediates Environmental Conditions during Development and Controls an Irreversible Commitment to Adulthood

Many animals can choose between different developmental fates to maximize fitness. Despite the complexity of environmental cues and life history, different developmental fates are executed in a robust fashion. The nematode Caenorhabditis elegans serves as a powerful model to examine this phenomenon because it can adopt one of two developmental fates (adulthood or diapause) depending on environmental conditions. The steroid hormone dafachronic acid (DA) directs development to adulthood by regulating the transcriptional activity of the nuclear hormone receptor DAF-12. The known role of DA suggests that it may be the molecular mediator of environmental condition effects on the developmental fate decision, although the mechanism is yet unknown. We used a combination of physiological and molecular biology techniques to demonstrate that commitment to reproductive adult development occurs when DA levels, produced in the neuroendocrine XXX cells, exceed a threshold. Furthermore, imaging and cell ablation experiments demonstrate that the XXX cells act as a source of DA, which, upon commitment to adult development, is amplified and propagated in the epidermis in a DAF-12 dependent manner. This positive feedback loop increases DA levels and drives adult programs in the gonad and epidermis, thus conferring the irreversibility of the decision. We show that the positive feedback loop canalizes development by ensuring that sufficient amounts of DA are dispersed throughout the body and serves as a robust fate-locking mechanism to enforce an organism-wide binary decision, despite noisy and complex environmental cues. These mechanisms are not only relevant to C. elegans but may be extended to other hormonal-based decision-making mechanisms in insects and mammals

Shell structure and orbit bifurcations in finite fermion systems

We first give an overview of the shell-correction method which was developed by V. M. Strutinsky as a practicable and efficient approximation to the general selfconsistent theory of finite fermion systems suggested by A. B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the "periodic orbit theory". We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called "superdeformed" energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).Comment: LaTeX, 67 pp., 30 figures; revised version (missing part at end of 3.1 implemented; order of references corrected

Sound modes in hot nuclear matter

The propagation of the isoscalar and isovector sound modes in a hot nuclear matter is considered. The approach is based on the collisional kinetic theory and takes into account the temperature and memory effects. It is shown that the sound velocity and the attenuation coefficient are significantly influenced by the Fermi surface distortion (FSD). The corresponding influence is much stronger for the isoscalar mode than for the isovector one. The memory effects cause a non-monotonous behavior of the attenuation coefficient as a function of the relaxation time leading to a zero-to-first sound transition with increasing temperature. The mixing of both the isoscalar and the isovector sound modes in an asymmetric nuclear matter is evaluated. The condition for the bulk instability and the instability growth rate in the presence of the memory effects is studied. It is shown that both the FSD and the relaxation processes lead to a shift of the maximum of the instability growth rate to the longer wave length region.Comment: 15 pages, 4 figures, submitted to Phys. Rev.

Semiclassical Trace Formulas for Noninteracting Identical Particles

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR

Prognosis of Differentiated Thyroid Cancer in Relation to Serum Thyrotropin and Thyroglobulin Antibody Status at Time of Diagnosis

BACKGROUND: Serum thyrotropin (TSH) concentration and thyroid autoimmunity may be of prognostic importance in differentiated thyroid cancer (DTC). Preoperative serum TSH level has been associated with higher DTC stage in cross-sectional studies; data are contradictory on the significance of thyroid autoimmunity at the time of diagnosis. OBJECTIVE: We sought to assess whether preoperative serum TSH and perioperative antithyroglobulin antibodies (TgAb) were associated with thyroid cancer stage and outcome in DTC patients followed by the National Thyroid Cancer Treatment Cooperative Study, a large multicenter thyroid cancer registry. METHODS: Patients registered after 1996 with available preoperative serum TSH (n=617; the TSH cohort) or perioperative TgAb status (n=1770; the TgAb cohort) were analyzed for tumor stage, persistent disease, recurrence, and overall survival (OS; median follow-up, 5.5 years). Parametric tests assessed log-transformed TSH, and categorical variables were tested with chi square. Disease-free survival (DFS) and OS was assessed with Cox models. RESULTS: Geometric mean serum TSH levels were higher in patients with higher-stage disease (Stage III/IV=1.48 vs. 1.02 mU/L for Stages I/II; p=0.006). The relationship persisted in those aged ≥45 years after adjusting for sex (p=0.01). Gross extrathyroidal extension (p=0.03) and presence of cervical lymph node metastases (p=0.003) were also significantly associated with higher serum TSH. Disease recurrence and all-cause mortality occurred in 37 and 38 TSH cohort patients respectively, which limited the power for survival analysis. Positive TgAb was associated with lower stage on univariate analysis (positive TgAb in 23.4% vs. 17.8% of Stage I/II vs. III/IV patients, respectively; p=0.01), although the relationship lost significance when adjusting for age and sex (p=0.34). Perioperative TgAb was not an independent predictor of DFS (hazard ratio=1.12 [95% confidence interval=0.74-1.69]) or OS (hazard ratio=0.98 [95% confidence interval=0.56-1.72]). CONCLUSIONS: Preoperative serum TSH level is associated with higher DTC stage, gross extrathyroidal extension, and neck node metastases. Perioperative TgAb is not an independent predictor of DTC prognosis. A larger cohort is required to assess whether preoperative serum TSH level predicts recurrence or mortality

Sex and sexuality: An evolutionary view

In this article, I first offer a summary of Darwin’s main ideas, especially relating to sex, and explain how these have been elaborated by more recent evolutionary scholars. I then give an account of the historical divergence between psychoanalysis and classical Darwinian thought, and describe how the early psychoanalyst Sabina Spielrein tried to counter this by addressing some biological themes in her work. Following a review of some contemporary attempts to bring psychoanalysis and evolutionary thought into alignment with each other, I make some suggestions regarding a view of sex and sexuality that would be sound in evolutionary terms while also being helpful in psychoanalytic ones